Estimation of a parameter vector restricted to a cone

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Abstract

We study estimation of a location vector restricted to a convex cone when the dimension, p, is at least 3. We find estimators which improve on the "usual" estimator (the MLE in the normal case) in the general case of a spherically symmetric distribution with unknown scale. The improved estimators may be viewed as Stein-type shrinkage estimators on the set where the usual unbiased estimator (in the unrestricted case) satisfies the restriction. The improved procedures have the extremely strong property of improving on the "usual" estimator uniformly and simultaneously for all spherically symmetric distributions.

Original languageEnglish (US)
Pages (from-to)121-129
Number of pages9
JournalStatistics and Probability Letters
Volume56
Issue number2
DOIs
StatePublished - Jan 15 2002

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Minimaxity
  • Restricted parameter spaces
  • Stein estimation

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